Quantitative Microscopy and Stereology
The ability to provide quantitative statements about micro-structural tissue properties is becoming increasingly important in biopharmaceutical research and development in diverse applications related to both safety- and efficacy pharmacology.
Typically it is of interest to make quantitative statements about number, length, surface area, and volume of structural features reflecting the condition of an organ. It may even be of interest to investigate second-order properties based on the (number or volume weighted) distribution of structural features.
There are real challenges and problems associated with the correct quantification of 3D structural properties of tissues, of which some are related to expensive and labor intensive procedures, others to common misconceptions about the ability to infer 3-D information from 2-D histological sections.
Here, it is important to realize that objects (e.g. cells) in 3-D space that are cut by a 2-D section, as with a histological section, will be seen as profiles. Such 3-D objects will be hit by the 2-D section with a probability in proportion to their size, specifically their height normal to the section. Therefore, the objects of interest do not have the same probability of being counted, which is also the reason that e.g. counting of profiles is a significantly biased measure of the number of objects in 3-D space.
Therefore it is important to use methods that allow for making inference from 2-D sections to 3-D objects. This can be done using certain geometrical probes and estimators. The combination of sampling and the application of a set of unbiased geometrical probes in 3-D are collectively referred to as design-based stereology.
The stereological methods typically applied rely on simple counting of the number of times a feature is intersected by a suitable geometrical probe. To ensure that the intersections are zero-dimensional, i.e. a point that can be counted, the dimension of the probe and the feature under investigation must always sum to three:                Points probe volume        Lines probe surface        Planes probe length        Volumes probe number (see FIG. 1)        
The disector principle is very useful for estimating the number of discrete objects as e.g. cells within a well defined reference space. This principle is widely used, and is perhaps the one area in which design-based stereology has had its largest impact to date. The principle also represents some special challenges seen from an automation point of view.
The major breakthrough in assumption-free, unbiased (stereological) counting was provided by the publication of the Physical Disector paper [Howard & Reed]. The disector consists of a pair of serial sections a known distance apart. The method relies upon the principle that if a particles transect (profile) is seen in one section and not the next, it is counted (this is a counting event).
The physical disector principle is used in a number of frequently occurring situations, 30 for example when the structures of interest are very large, if the tissue is not sufficiently transparent to allow for the use of an optical disector, or when the staining, whatever reason, cannot penetrate sufficiently deep into the tissue under investigation.
The physical disector uses as the name suggests, at least two adjacent or serial physical sections from the tissue under investigation.
FIG. 2 illustrates two corresponding fields of view sampled from two registered sections of tissue. Using the upper image as reference and the lower image as look-up counting events are identified.
In practice, it is found that most of the time spent in applying a physical disector is dedicated to registering the two sections. Therefore, in order to increase the overall efficiently, counting is done both ways—Le. by reversing reference and look-up.
Image registration of sections required for the physical disector method rely on spatial mapping and based on both structural/textural and intensity differences between two images. Many types of distortions can be present between images of the two sections to be registered. The task of registration is to select the transformation method, which will remove only the spatial distortions between the images due to difference in acquisition and not due to differences in scene characteristics. With the help of geometric transformations, the spatial relationships between pixels in the images can be modified. A geometric transformation consists of two basic operations: a spatial transformation and a gray-level interpolation. The spatial transformation defines the mapping of the new pixel locations in the output image according to the pixel locations in the input image. There are several methods that can be used for gray level interpolation. For example the nearest neighbor approach, cubic convolution interpolation and bilinear interpolation. For Gray level interpolation, the new pixel coordinates (x1, y1) are calculated by means of the spatial transformation. Digital images are used, therefore the original coordinates have integer values. Depending on the values of the parameters, the new coordinates, (x′,y′) can become noninteger values. Since the distorted image i2 is digital, its pixel values can only be defined at integer coordinates. Thus using noninteger values for x′ and y′ causes a mapping into locations of i2 for which no gray levels are defined. The gray level values of these noninteger points should be based on the integer point locations around the noninteger points.
An Unbiased counting frame comprising an area of an image field is preferably used in the process of enumeration counting events in a given disector pair. The unbiased counting frame has an acceptance boundary and a “forbidden” boundary, as shown in FIG. 11. Any particles intersecting the “forbidden” line may not be counted. Particles which are situated inside the counting frame or those that intersect with the acceptance line but not the “forbidden” line may be counted. In FIG. 1, the counting is carried out according to these simple rules.
In the context of the physical disector, counting events are included according to these rules. Thus a cell nucleus is only counted if it is a counting event and fall inside the counting frame as described above. It is only a counting event if it is found in the reference image, but not in the look-up image.
The total amount micro-structure in a volume, such as e.g. number of cells, is based on estimation principles. An estimator is a tool that, given data, is capable of providing an estimate. Typically, the estimators used in stereology provide estimates of the amount of a feature per unit reference volume. Typically the following ratio quantities, generally known as densities, are used:    Volume density: Vv The volume proportion of one phase within a reference volume    Surface density: Sv The area of an interface within a unit reference volume    Length density: Lv The length of a linear feature within a unit of reference volume    Numerical density: Nv The number of discrete objects in a unit reference volume
In biological systems, the definition of the reference space is crucial. The fundamental sampling unit (FSU) is related to the organism/organ of interest. It is only in the knowledge of the size of the reference space that the nature of any variation or lack thereof can be fully understood.
In many situations this can be accomplished using advanced image segmentation techniques, that allows for simple test of whether or not a geometrical probe intersects with a given (segmented) structure in field-of-view.
Stereology software is commercially available. The most Widespread packages are probably the StereoInvestigator by MicroBrightfield and the CAST system by Visiopharm (taken over by Visiopharm A/S from Olympus Denmark A/S).
Even with careful planning and using the physical disector principle, the procedure of obtaining quantification based on design based stereology is still time consuming and labor intensive and certainly not ideally suited for screening purposes or even moderate-volume routine purposes.
Human operators are required for accessing the physical slide and mounting it on a stage under the microscope. Even with software controlling the systematic random sampling, it is necessary to wait while the stage is moving to the next sampling position. Significant time is used for focusing and other adjustments before counting can commence.
Thus, a major obstacle so far has been the inability to deal with microscope slides in the digital domain.